Exploding solutions for a nonlocal quadratic evolution problem
Exploding solutions for a nonlocal quadratic evolution problem
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DOI：
10.4171/rmi/602
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发表时间：
2010-04
影响因子：
1.2
通讯作者：
Dong Li;José L. Rodrigo;Xiaoyi Zhang
中科院分区：
文献类型：
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作者：
Dong Li;José L. Rodrigo;Xiaoyi Zhang
我们考虑一个非线性抛物型方程的分数扩散，这是由于模拟细菌的趋化性。我们证明了适定性，连续性准则，和光滑的局部解决方案。在排斥的情况下，我们证明了整体适定性的Sobolev空间。最后，在吸引情形下，证明了对于一类光滑初值，相应解的L-x（无穷）范数在有限时间内爆破。这解决了Biler和Woyczynski [8]留下的问题。
We consider a nonlinear parabolic equation with fractional diffusion which arises from modelling chemotaxis in bacteria. We prove the wellposedness, continuation criteria, and smoothness of local solutions. In the repulsive case we prove global wellposedness in Sobolev spaces. Finally in the attractive case, we prove that for a class of smooth initial data the L-x(infinity)-norm of the corresponding solution blows up in finite time. This solves a problem left open by Biler and Woyczynski [8].